Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them from MSL. To make the book accessible to readers from different disciplines, whilst maintaining precision, the author has supplied detailed step-by-step proofs, avoiding difficult arguments, and continually motivating the material with examples. Consequently this can be used as a reference, for self-teaching or for first-year graduate courses.
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"The book is well motivated and is easy and pleasant to read." Mohamed Amer, Mathematical Reviews
Book Description
Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to work.
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Inside This Book
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First Sentence:
Second order logic (SOL) is distinguished first order logic in that it has relational as well as individual variables, and both types of variables can be quantified. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
untyped relations, constructible part, membership relation symbols, standard second order logic, background set theory, weak second order logic, unary relation variables, sound calculus, second order calculus, coincidence lemma, deductive calculus, syntactical translation, selector operator, definable closure, complete calculus, mathematical universe, dynamic algebras, comprehension schema, schema axioms, first order relations, second order language, relational universes, simple type theory, normal modal logic, sequent rules Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Use, Proof Assume, Definition of A-definable, Proof Obvious, The Zermelo-Fraenkel New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Second order logic (SOL) is distinguished first order logic in that it has relational as well as individual variables, and both types of variables can be quantified. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
untyped relations, constructible part, membership relation symbols, standard second order logic, background set theory, weak second order logic, unary relation variables, sound calculus, second order calculus, coincidence lemma, deductive calculus, syntactical translation, selector operator, definable closure, complete calculus, mathematical universe, dynamic algebras, comprehension schema, schema axioms, first order relations, second order language, relational universes, simple type theory, normal modal logic, sequent rules Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Use, Proof Assume, Definition of A-definable, Proof Obvious, The Zermelo-Fraenkel New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 67
books:
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2
books
cite this book:
- Mathematical Logic (Graduate Texts in Mathematics) by J.D. Monk on 4 pages
- Mathematical Logic (Undergraduate Texts in Mathematics) by H.-D. Ebbinghaus on page 78, Back Matter (1), and Back Matter (2)
- Modal Logic (Cambridge Tracts in Theoretical Computer Science) by Patrick Blackburn in Back Matter (1), and Back Matter (2)
- Cylindric Algebras, Volume I (Studies in Logic and the Foundations of Mathematics) (Pt. 1) by Sahra Sedigh in Back Matter
- A Companion to Modal Logic by G. E. Hughes in Back Matter
See all 67 books this book cites
- Deductive and Object-Oriented Databases: Third International Conference, DOOD '93, Phoenix, Arizona, USA, December 6-8, 1993. Proceedings (Lecture Notes in Computer Science) by Stefano Ceri on page 66
- ICDT'86: International Conference on Database Theory. Rome, Italy, September 8-10, 1986. Proceedings (Lecture Notes in Computer Science) by Giorgio Ausiello on page 27
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